State whether or not each figure has rotational symmetry.

a) scalene triangle
b) equilateral triangle
c) rectangle
d) square
e) regular hexagon

i'm not sure, but i think all of them do except for the scalene triangle and maybe the rectangle.

To determine if a figure has rotational symmetry, we need to analyze if it looks the same after rotating it by certain angles. Let's go through each figure:

a) Scalene Triangle: A scalene triangle is a triangle with all sides and angles of different lengths and measures. Since its sides and angles are not equal, it does not have rotational symmetry.

b) Equilateral Triangle: An equilateral triangle is a triangle with all sides and angles equal. It has rotational symmetry. To determine the extent of its rotational symmetry, let's analyze it. By rotating it 120 degrees counterclockwise, it will still look the same. Similarly, rotating it 240 degrees counterclockwise will bring it back to its original position. Therefore, an equilateral triangle has rotational symmetry of order 3, meaning it looks the same after a 120-degree rotation.

c) Rectangle: A rectangle is a quadrilateral with four right angles. It can have rotational symmetry, but the extent of this symmetry depends on the dimensions of the rectangle. Let's analyze it further. If the rectangle is a square (all sides equal), it has rotational symmetry of order 4, meaning it looks the same after a 90-degree rotation clockwise or counterclockwise. However, if it's a rectangle with unequal sides, it does not have rotational symmetry since different side lengths create an uneven figure after rotation.

d) Square: A square is a quadrilateral with four equal sides and four right angles. It has rotational symmetry. By rotating it 90 degrees counterclockwise or clockwise, it will look the same. Therefore, a square has rotational symmetry of order 4.

e) Regular Hexagon: A regular hexagon is a polygon with six equal sides and six equal angles. It has rotational symmetry. By rotating it 60 degrees counterclockwise, it will look the same. Similarly, rotating it 120, 180, 240, or 300 degrees counterclockwise will bring it back to its original position. Therefore, a regular hexagon has rotational symmetry of order 6.

In summary:
a) Scalene Triangle: No rotational symmetry.
b) Equilateral Triangle: Rotational symmetry of order 3.
c) Rectangle: Depends on its dimensions. Unequal sides have no rotational symmetry, while a square has rotational symmetry of order 4.
d) Square: Rotational symmetry of order 4.
e) Regular Hexagon: Rotational symmetry of order 6.